Calculus and Fundamentals

1. Calculus
2. Mean Value Theorem
3. Fundamental Theorem of Calculus
4. Fundamental Theorem of Algebra
5. Big "O" Truncation Error
6. Complex Numbers
7. Maclaurin and Taylor Series

 

Solution of Differential Equations

1. Euler's Method for O. D. E.'s
2. Taylor Series Method for D.E.'s
3. Runge-Kutta Method
4. Runge-Kutta-Fehlberg Method
5. Adams-Bashforth-Moulton Method
6. Milne-Simpson's Method
7. Predictor-Corrector Methods for O.D.E.'s
8. Shooting Methods for O.D.E.'s
9. Finite Difference Method for O.D.E.'s
10. Galerkin's Method
11. Lotka-Volterra Model
12. Pendulum
13. Projectile Motion
14. Lorenz Attractor
15. Duffing Equation
16. Belousov-Zhabotinskii Model
17. Hodgkin-Huxley Model
18. Michaelis-Menten Model
19. van der Pol System
20. Harvesting Model
21. Spring Mass Oscillations
22. Compartment Model
23. Earthquake Model
24. Matrix Exponential
25. Stiff Differential Equations
26. Autonomous Systems
27. Series Solutions & Frobenius Method
28. Airy Functions
29. Bessel Functions
30. Exact Differential Equations
31. Homogeneous Linear Differential Equations
32. Separable Differential Equations
33. Variation of Parameters
34. Laplace Transforms

 

Solution of Partial Differential Equations

1. Finite Difference Method
2. Crank-Nicolson Method
3. Elliptic PDE's
4. Vibrating Drum
5. Vibrating String
6. Dirichlet Problem
7. Harmonic Functions

(c) John H. Mathews 2005